If you want to travel solo/female I think it's more comfortable not to go to an AI resort, which usually caters more to couples, rather to travel independently.

I go to Mexico (Puerto Vallarta) every year, most often by myself, I've never felt "weird". Lots of people vacation solo there. It's a "local authentic safe" area.

I have to agree, based on what you described, I don't think an AI resort will fit your needs. We've been to 16 of them throughout the Caribbean and Mexico in all price ranges. There are a few adult only resorts, but they really cater to couples. The family resorts are just that, full of families.

You might look at Aruba. The smaller hotels on Eagle Beach would fit. There is no selling or harassing on the beaches. Tons or really great restaurants and bars. Easy, cheap public transportation. I wouldn't feel out of place there as a single woman. I would also suggest Grand Cayman or Turks & Caicos.

If you go the week before or the week after either of those 2 holidays, you will find better prices and lower crowds. However, September is consider hurricane season. You would probably be fine in Aruba during that time frame.

I tend to agree that most adults only AI's cater to couples but take a look at the adult only Iberostar Grand in Montego Bay, Jamaica. We were there a couple of years ago (as a couple) but there were definitely a few singles and we even ran into a couple of families who had their adult children with them. The nice thing about the Iberostar is that they not only keep vendors off the beach but they even keep children off of the beach in front of the adults only section. They also have a different show every night (which were very entertaining) and an excellent piano bar. I can still remember the fabulous local woman singing Bob Marley songs. She was stunningly good. The food was also very good with only a couple of just goods. I don't think you would feel out of place at all and their beach service was good and unobtrusive so you can read to your heart's content.

And I also agree on the places mentioned by suze and KVR. I think there might even be an AI or two on Eagle Beach, Aruba if you still want to go that route. Or at least there used to be.